Abstract

We provide new proofs of two key results of p-adic Hodge theory: the Fontaine-Wintenberger isomorphism between Galois groups in characteristic 0 and characteristic p, and the Cherbonnier–Colmez theorem on decompletion of \((\varphi , \Gamma )\)-modules. These proofs are derived from joint work with Liu on relative p-adic Hodge theory, and are closely related to the theory of perfectoid algebras and spaces, as in the work of Scholze.

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